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In this article, we show that the predual $\mathcal{G}_w(U)$ of the weightedspace of holomorphic functions has the $\mathcal{I}$- approximation property ifand only if $E$ has the $\mathcal{I}$- approximation property, where$\mathcal{I}$ is a suitably chosen operator ideal, and $\it{w}$ is a radialweight defined on a balanced open subset U of a Banach space $E$.

Characterizations of approximation properties defined by operator ideals in the predual of weighted Banach spaces of holomorphic functions